数学季刊 >

2020 , Vol. 35 >Issue 3: 278 - 289

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.03.003

带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法

展开
  • 1. College of Mathematics and Information, South China Agricultural University2. School of Mathematics and Statistics, Yangtzc Normal University
LIN Hai-xin(1996-), female, native of Zhanjiang, Guangdong, engages in partial di erential equation; FANG Shao-mei(1964-), female, native of Anhui, a professor of South China Agricultural University, engages in partial di erential equation.

收稿日期: 2020-05-06

  网络出版日期: 2020-10-22

基金资助

Supported by the Nation Natural Science Foundation of China (No.11271141)； the Chongqing Science and Technology Commission (cstc2018jcyjAX0787)；

收起

Finite Di erence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition

Expand
  • 1. College of Mathematics and Information, South China Agricultural University2. School of Mathematics and Statistics, Yangtzc Normal University
LIN Hai-xin(1996-), female, native of Zhanjiang, Guangdong, engages in partial di erential equation; FANG Shao-mei(1964-), female, native of Anhui, a professor of South China Agricultural University, engages in partial di erential equation.

Received date: 2020-05-06

  Online published: 2020-10-22

Supported by

Supported by the Nation Natural Science Foundation of China (No.11271141)； the Chongqing Science and Technology Commission (cstc2018jcyjAX0787)；

Fold

摘要

In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t2+ h2）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme. 

本文引用格式

林海欣 , 房少梅, . 带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法[J]. 数学季刊, 2020 , 35(3) : 278 -289 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.003

Abstract

In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t2+ h2）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme. 

Key words： fractional advection-dispersion equation, Riesz fractional derivative, fractional ; central difference, stability, convergence

Options
文章导航

/

〈 〉

版权所有 © 《数学季刊》编辑部
地址：河南省开封市明伦街85号河南大学数学季刊编辑部
电话：0371-23881698　E-mail: sxjk@henu.edu.cn　QQ: 2454327236
本系统由北京玛格泰克科技发展有限公司设计开发　技术支持：support@magtech.com.cn